The number of people entering a competition over a number of weeks was 19, 16, 10, 15, 11, 17, 26, 239, 16, 10, 15, 11, 17, 26, 23 and 16.a Calculate the mean, median and mode for this data.b What is the effect on the mean, median and mode of adding 5 to each score?c Calculate the mean, median and mode with these extra people entering the competition

a) To calculate the mean, you add up all the numbers and then divide by the number of numbers.

Mean = (19 + 16 + 10 + 15 + 11 + 17 + 26 + 239 + 16 + 10 + 15 + 11 + 17 + 26 + 23 + 16) / 16 = 484 / 16 = 30.25

The median is the middle number in a sorted list of numbers. If there is an even number of numbers, the median is the average of the two middle numbers.

First, sort the numbers: 10, 10, 11, 11, 15, 15, 16, 16, 16, 17, 17, 19, 23, 26, 26, 239

The median is the average of the 8th and 9th numbers, so Median = (16 + 16) / 2 = 16

The mode is the number that appears most frequently. In this case, the number 16 appears three times, more than any other number, so the mode is 16.

b) Adding 5 to each score will increase the mean, median and mode by 5.

Mean = 30.25 + 5 = 35.25 Median = 16 + 5 = 21 Mode = 16 + 5 = 21

c) To calculate the mean, median and mode with the extra people, you add 5 to each original number and then calculate as before.

Mean = (24 + 21 + 15 + 20 + 16 + 22 + 31 + 244 + 21 + 15 + 20 + 16 + 22 + 31 + 28 + 21) / 16 = 539 / 16 = 33.6875

Sort the numbers: 15, 15, 16, 16, 20, 20, 21, 21, 21, 22, 22, 24, 28, 31, 31, 244

Median = (21 + 21) / 2 = 21

The mode is now 21, as it appears three times, more than any other number.